Final answer:
The magnitude of the pedestrian's displacement is approximately 14.0 km, and the direction is approximately 67.3° north of east.
Step-by-step explanation:
The magnitude of the pedestrian's displacement can be found using the Pythagorean theorem. The displacement is the hypotenuse of a right triangle formed by the two paths. Using d₁ and d₂ as the sides of the triangle, the magnitude of the displacement, d, can be found by:
d = √(d₁² + d₂²)
Plugging in the values of d₁= 5.6 km and d₂ = 12.8 km, we get:
d = √((5.6 km)² + (12.8 km)²)
Calculating this expression gives us a displacement of approximately 14.0 km.
The direction of the pedestrian's displacement can be found using trigonometry. We can use the inverse tangent function to find the angle in degrees north of east. Using the same right triangle formed by the two paths, we can calculate the angle, θ, by:
θ = tan⁻¹(d₂ / d₁)
Plugging in the values of d₁= 5.6 km and d₂ = 12.8 km, we get:
θ = tan⁻¹((12.8 km) / (5.6 km))
Calculating this expression gives us an angle of approximately 67.3° north of east.